You can force mint by putting some of the root in a container and keeping it in a gentle heat indoors or in a greenhouse. It soon shoots and you should be able to keep it going all winter. Lay a length of root in a seed-tray, cover with compost, keep moist and warm. I think your problem is over crowding coupled with it being the end of the season. However, if it is rust, chuck it away and scrounge some more to grow for next year.

The old way of growing mint was to grow it in an old sink, which was then buried. It is deep and big enough to get a good amount of growth, without letting it take over the whole herb patch, which it will do given half a chance.